Elliptic curve isogeny class with LMFDB label 481338.bc (Cremona label 481338bc)

• Label: 481338.bc
• Number of curves: $2$
• Conductor: $481338$
• CM: no
• Rank: $1$

Elliptic curves in class 481338.bc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
481338.bc1	481338bc2	\([1, -1, 0, -1363137, 613093949]\)	\(-117615821673598875/40164914816\)	\(-95658488217122688\)	\([]\)	\(9144576\)	\(2.2299\)	\(\Gamma_0(N)\)-optimal^*
481338.bc2	481338bc1	\([1, -1, 0, 9663, 3149757]\)	\(30541139380125/1331551010816\)	\(-4350177152335872\)	\([]\)	\(3048192\)	\(1.6805\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 481338.bc1.

Rank

The elliptic curves in class 481338.bc have rank \(1\).

Complex multiplication

The elliptic curves in class 481338.bc do not have complex multiplication.

Modular form 481338.2.a.bc

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.